


Staircase of Primes [大人の階段]

by Anonymous



Category: Magia Record: Puella Magi Madoka Magica Side Story, Mahou Shoujo Madoka Magika | Puella Magi Madoka Magica
Genre: Age Difference, Coitus Interruptus, F/F, Femdom, Futanari, Large Cock, Light Bondage, Math Kink, Table Sex, Vaginal Sex
Language: English
Status: Completed
Published: 2020-03-24
Updated: 2020-04-27
Packaged: 2021-02-28 17:54:08
Rating: Explicit
Warnings: Underage
Chapters: 2
Words: 2,769
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/23301217
Author URL: https://archiveofourown.org/
Summary: When Touka stumbles upon Tsuruno alone in Mikadzuki villa, in the midst of solving one of the greatest unsolved problems in the math discipline, she finds the opportunity to make up for past misdeeds and apologize.Said apology may or may not involve bending Tsuruno over a table and fucking her senseless.
Relationships: Satomi Touka/Tamaki Ui, Satomi Touka/Yui Tsuruno
Comments: 1
Kudos: 40
Collections: Anonymous





	1. Chapter 1

‘Onee-sama! Ui! I’m here to visit!’

Touka’s voice preceded her only by seconds as her small figure burst into the doorway. But instead of Iroha, the only person in the living room of the Mikadzuki Villa was a brown-haired girl staring at a tablet on the coffee table.

‘Oh, hi,’ said the girl, who looked up after Touka had gone in. ‘I’m sorry, but Iroha and the rest are out buying groceries.’

‘Saikyo-san~’ said Touka in a teasing tone as she sauntered towards her. Memories of ill-defined apprehension and pleasure tickled the back of Tsuruno’s brain as she heard her voice. ‘What are you doing here alone, then?’

‘Ah,’ said Tsuruno, shaking off that vague feeling. ‘I have an idea about the Riemann hypothesis. Do you know what that is?’

Touka put a hand to her hip, deep in thought. She had studied complex analysis since it had multiple applications in modern physics, and she had heard of the Riemann zeta function in passing, but she didn't pay much attention to it.

‘Not really,’ said Touka. ‘That's closer to pure mathematics, isn’t it? I didn’t think I’d need it.’ She moved behind Tsuruno, and her chin almost touched her shoulder as she looked at the tablet on the table. ‘So, what is it about? Something about prime numbers, right?’

‘Hmmm.’ Tsuruno was thinking, but her thoughts were somewhat perturbed due to how close Touka was. ‘How much time do you have?’

‘Mifuyu is out, and I have nothing to do, which is why I came here to play.’ She took a step back and beamed at Tsuruno. ‘So I have aaaall day to listen to you.’

Tsuruno turned her back on the table and faced Touka. She coughed once melodramatically and said, ‘Well, then. Get ready to listen to a little history. The Riemann hypothesis is the greatest unproven answer to this question: how are prime numbers distributed on the number line? His was a roundabout way of doing it, bringing the tools of complex number analysis to the world of integers, but it is also the most accurate, and can help answer a lot of other questions about prime numbers.’

She then went on to discuss the Ancient Greek mathematician Eratosthenes and his sieve, Gauss's prime-counting function and his logarithmic estimation of said function, and then the more accurate integral version of his estimate.

‘Now, the funny thing is,’ Tsuruno said, turning back to the tablet to bring up a table of values, ‘for the first few quintillion numbers, the limit of what current technology can compute manually, Gauss’s estimate overshot the number of primes by about a square root of its own value. So what if you can adjust his equation by subtracting…’

Touka had taken an interest in Tsuruno mainly because she had both the intelligence of Nemu and the kindness of Ui. Seeing her display those traits up close, in such an intimate setting, caused Touka's body to change.

Her magic-suppressing bracelet crackled a little, and Tsuruno felt something something long and hard poking her in the back.

‘Uh, Touka-chan,’ said Tsuruno, a hint of apprehension in her voice. ‘What’s that?’

‘Saikyo-san,’ replied Touka, her voice now a husky whisper, ‘do you know what a Dirac delta function is?’

‘Isn’t it a piecewise function that’s zero at all values except a particular one? And at that value it's a horizontal line.’

‘That's correct,’ purred Touka as she lifted Tsuruno’s skirt from behind. ‘And you just entered the correct value for my Dirac delta function.’

Tsuruno squirmed as she felt something enter her.

‘I’m sorry if I'm being selfish, Saikyo-san,’ Touka whispered. ‘I just can help thinking how cute you are.’

As Touka forced her way into the older girl, Tsuruno's mind recalled a scene she thought she had left behind.

She remembered the softness of a luxurious carpet on her knees and legs.

She remembered the hardness of a wooden table on which her entire upper body rested.

She remembered the fancy antique decorations in a room of an opulent hotel, the traces of a rumour's barrier covering its walls and ceiling, and—

Tsuruno gasped as she felt Touka go all the way inside her.

—the same feeling of a young girl having her way with her body.

‘Touka-sama,’ said Tsuruno. Her voice was monotone, her eyes lifeless.

‘No, Saikyo-san,’ said Touka, concern furrowing her brows. ‘We’re no longer at Fendthope.’ She slowly pulled her hips back. ‘We’re at a place where you belong.’

‘Where I belong?’ mimicked Tsuruno like a confused child, but then her eyes took in her surroundings. A comfortable sofa in front of the television. A spacious dining table where her familiar mug rested. The rather small but well-stocked kitchen.

‘Mikadzuki,’ said Tsuruno. Life returned to her voice and her eyes.

Touka slowly ground herself in all the way once more, and Tsuruno moaned in pleasure.

‘Consider this my personal apology,’ Touka breathed directly into her ears. Her chest now rested on Tsuruno’s back; her arms wrapped around her waist.

‘Continue your lecture, Tsuruno-sensei.’ It was the first time that she had called her by her name.

‘Right, where were we?’ said Tsuruno. She struggled to keep her voice even, but succeeded for most part. Her hands fumbled around the table top, looking for the tablet she had been using.

‘Here it is,’ Touka said. Her right hand left Tsuruno’s hips and slid the tablet over to her.

‘That”s right. Gauss's logarithmic integr—AHH!”

This time, Touka had thrust herself all the way in at once.

‘Where does Riemann come in, sensei?’ she asked as she slowly pulled out. Tsuruno wrapped tightly wrapped around her, reluctantly letting her go, and even Touka found herself gasping.

‘I know you know this, but Riemann is famous for things other than this hypothesis.’

‘Riemannian manifolds are important objects of study in general relativity,’ Touka confirmed.

‘But he wrote one—and it's a short one—paper on number theory, where he defined a correction term that would make Gauss’s estimate be exactly equal to the prime counting function.’

‘Exactly equal? But the logarithmic integral is a smooth curve, and the prime counting function is a bunch of horizontal and vertical lines arranged like a flight of stairs. How can a smooth curve be made to look like straight lines—That’s right! Fourier analysis!’

‘That's correct. Fourier analysis allows us to approximate a function composed of straight lines: a square wave, a sawtooth wave, even the Dirac delta fuMMMMMMMM~!’

Tsuruno covered her mouth to suppress a loud moan, and her body, bereft of support, collapsed onto the table. Her head rested beside the tablet, almost like a pillow; a bit of drool spilled onto it.

‘Saikyo-san, are you okay?’ said Touka. There was concern in her voice, but her lips formed a smile, and she picked up the pace of her thrusting.

‘Ah, ahn!’ Tsuruno was jolted back to wakefulness. ‘Touka-chan, I just came! Be gentler!’

‘So what does the Riemann zeta function have to do with all this?’ asked Touka, ignoring Tsuruno’s request. ‘It seems weird that there's a connection between an infinite series of fractions and prime numbers, and you make it weirder by adding complex numbers.’

‘The first—NN!—strong connection between prime numbers and the zeta—gah!—function was when Euler proved that it can be expressed as a product of reciprocals containing all the primes—right there!’

There was no doubt that Tsuruno’s body was more sensitive than before. She could no longer talk straight without gasping, groaning, or clenching her fists, and Touka’s furious pace didn't help things.

‘And Riemann’s correction term uses the non-trivial—mmmm~—zeros of the zeta function as the coefficients of a Fourier series.’

‘Hmm, that seems all sewn up. So why is it still a hypothesis?’

‘The first few trillion non-trivial zeros of—OHH!—the zeta function are all complex numbers whose real part is 1/2. But what mathematicians want to know is, are they all like that?’

At this point, Tsuruno’s words were coming out in gasps.

‘Because Riemann's original—‘

‘Saikyo-san,’ Touka said with a strained voice. ‘I’m almost there.’

‘—correction term depends onAAAAAAAAAAAAAAAAH~~!’

Touka collapsed onto Tsuruno's back. Tsuruno's hands clenched the edge of the table, willing her arms to support her body as waves of pleasure washed over her. At that exact moment, the door swung open.

‘So, Tsuruno, did you—’ Yachiyo walked in, holding a bag of groceries and stopped in her tracks upon seeing the tangle of bodies sprawled on her coffee table.

‘Touka-chan…’ Iroha’s voice carried a mixture of embarrassment and consternation.

But the real ticking bomb was the little girl who entered last.

‘Nya! Ui! A horrified Touka tried to stand up, but a jolt of numbness ran through her legs, making her stumble and fall flat on carpet.

Tsuruno was slow to react, but she hurriedly fixed her skirt and sat upright, a sheepish smile plastered on her face.

Ui continued to glare silently at Touka—more specifically, at the suspicious bulge on her unkempt skirt. The rest of the newcomers awaited her explosion with bated breath.

‘TOUKA-CHAN!’ she screamed, throwing the loaf of bread in her hand at Touka’s face. ‘You pervert!’

A crackle of energy passed through Touka’s bracelet, and the bulge disappeared.


	2. Chapter 2

Touka woke up with a start.

Her attempts to get out of the bed did not last long, as the handcuffs that attached her wrists to the headboard announced their presence with a clink and a backwards tug.

‘I knew it,’ she half-muttered, half-sighed.

She should have been suspicious right from the start.

Right when Ui, an angelic smile plastered on her face, asked her if she would like to sleep over at Mikadzuki while her sister and the others were away on KMU duties.

Or right when Nemu, normally verbose, said that she couldn't come because she had something to do, and then clammed up when Touka asked her what it was.

Or when Ui volunteered to cook dinner for that two of them—‘I’ve been learning from onee-chan!’—and urged Touka to just sit by the living room sofa.

She should definitely have been suspicious when Ui intently watched her take a bite of the karaage, even while her chopsticks hung unmoving over her own bowl

Ui had scared Nemu off. She had put something in the food that knocked me unconscious.

It didn't take a great detective, like some of the ones Nemu enjoyed reading about, to figure out what happened. (By the way, Touka didn't like those novels because she thought they didn't properly use the clues the author had laid out to resolve the cases. In other words, she focused on the wrong details and often came to the wrong conclusion.) The details were less like clues in a mystery, but more like variables in an equation.

And to Touka, the answer to that equation was clear:

_She’s still mad for what I did with Saikyo-san._

‘I’M REALLY SORRY, UI! FORGIVE ME!’

She directed this apology at the small shadowy figure on a chair in front of the bed.

The figure hmmed.

‘Onee-chan said that while saying sorry is important, a better way to show that we're sorry is through our actions.’

Touka had trouble seeing past the bed, and the strange lighting arrangement of the room didn’t help matters.

A minute of silence passed, broken only by Touka’s increasingly raspy breathing. Sweat drenched the collar of her nightdress.

‘Satomi Touka.’

Ui’s voice wasn’t particularly loud, but the way it shattered the silence made it feel like a thunderclap to Touka’s ears. She sat up more straightly out of instinct.

‘I’ve heard that you’ve been a very—’

Ui stood up and took a step towards the bed.

‘—bad—’

Another step.

‘—girl.’

Another step, and now she was at the foot of the bed.

From the sound of her voice, Touka could tell that Ui wasn’t angry. Touka could handle anger. She was used to it. She could understand why people would be angry with her. It was the natural consequence of being someone who did what she wanted, without needing anyone’s permission or acceptance.

No, Ui was disappointed. Ah, that one was different. She wasn’t used to disappointing people. In fact, the only people she had disappointed at one point or another in her life were… onee-sama and Ui.

Ui took a seat by her feet. Touka could now see her face, and immediately wished she couldn’t. She wore a maternal smile that didn’t reach her eyes, and this expression, coupled with terrifying aura that emanated from her, unsettled Touka more than if she had been in a paroxysm of rage.

_What is she planning to do?!_ Touka screamed in her mind as she tugged at the handcuffs chaining her to the bed. The only reward she got for her effort was furious jingling.

‘I saw that you got something while I was away,’ said Ui as she tugged at the hem of Touka’s nightdress. ‘Why don’t you take it out now?’

‘Wh-What do you mea—nya!’ Touka shrieked as Ui pulled up the hem, revealing her plain white underwear.

‘Where is it, Touka-chan?’ said Ui as she stuck her left hand inside Touka’s panties. Touka squirmed as Ui’s fingers found its way inside her.

‘Ui!’ Touka screamed, her eyes closed, her face flushed. ‘Please stop!’

‘Not—’

Her finger slid in deeper.

‘—until—’

It slid out a little.

‘—you—’

Ui’s finger thrust her finger all the way in.

‘—show me.’

Touka screamed incomprehensibly. Her back arched uncomfortably; her entire body trembled. Rivulets of wetness trickled down her thighs.

‘Why won’t you show me?’ Ui said, her voice oozing with dismay. ‘You’d show it to Tsuruno-san, but not to one of your oldest friends?’

‘Ui…’ Touka whimpered. Her body collapsed back onto the bed; she dangled limply from her shackled arms. She tried to apologise, but she her mind was so fuzzy that she couldn’t muster the concentration to string more than two words together.

‘Maybe I need to do this.’ Ui jumped onto the bed, her legs straddling Touka’s body, and, in one smooth motion, slipped out of her nightdress. Now clad in nothing but her pink panties, she bent over Touka until her face was right on top of hers. They could feel each other’s breath tickling their noses.

‘Touka-chan, let’s play.’

Touka shut her eyes with such intensity that her eyelids seemed to burrow into her socket. There was a crackle of electricity from Touka’s bracelet, and then Ui felt something poking her in the thigh.

‘There we go,’ said Ui as she turned her body to face Touka’s legs. ‘Why, it’s already up. Touka-chan, you naughty kitten.’

Ui wrapped her hands around it. Touka tensed at the sudden touch to her sensitive penetrator, but Ui sat down on her face before she had the chance to get up.

‘This is embarrassing, so no peeking.’

Touka mumbled something into Ui’s panties, but she paid it no mind as she continued stroking her. Overwhelmed by the myriad sensations assaulting her brain, she tried to focus her mind on something else.

She tried computing the exact solution to the Einstein field equations of a rotating body.

—Ui’s fingers twirled around the head.

How about the time-dependent Schrödinger equation of a harmonic oscillator?

—Ui’s fingers slid up and down the shaft.

_It’s not working!_ Touka tried to shout, but all that came out was a muffled shriek.

‘It tickles when you do that, Touka-chan.’

Touka was close to her limit. Ui must have noticed it, too, as she pinched the Satomi penetrator hard.

‘Not yet, Touka-chan.’

Another muffled scream came from Touka, Even Ui was starting to feel funny, as evidenced by the wetness sticking to her nose and mouth.

Ui’s voice came in gasps as she said, ‘Just a bit more, Touka-chan.’

Touka felt as if she was experiencing time dilation. Seconds stretched to minutes; every stimulus strained her senses. At last, when she felt that she could endure it no longer, Ui wrapped her lips around the Satomi penetrator.

‘Come, Touka-chan!’ she said as she plunged the penetrator deeper into her tiny mouth.

A torrent gushed from Touka. The two shared a drawn-out scream of ecstasy, and then lay motionless for a long while. Finally, Ui broke the silence.

‘Touka-chan, are you really sorry?’

‘Yes.’

‘Then promise me you’ll never bring out that thing again.’

‘I promise, Ui.’

‘—unless onee-chan or I tell you to.’

Touka could only sigh in reply. She wondered if she could endure being a plaything of the Tamakis again.


End file.
